A dynamic random access game with energy constraints

We study a dynamic random access game with a finite number of opportunities for transmission and with energy constraints. We provide sufficient conditions for feasible strategies and for existence of Nash-Pareto solutions and show that finding Nash-Pareto policies of the dynamic random access game is equivalent to partitioning the set of time slot opportunities with constraints into a set of terminals. We further derive upper bounds for pure Nash-Pareto policies, and extend the study to non-integer energy constraints and unknown termination time, where Time Division Multiplexing policies can be suboptimal. We show that the dynamic random access game has several strong equilibria (resilient to coalition of any size), and we compute them explicitly. We introduce the (strong) price of anarchy concept to measure the gap between the payoff under strong equilibria and the social optimum.